Homework 05 BIOS 517D/Biostats
1. What are the four linear regression assumptions? Explain each assumption in at most two sentences; use plain English. 2. Read the bodyfat data set into SAS. The
relationship of interest is between body fat percentage (as measured using Siri���s formula) and abdominal girth (cm). The model is BODYFATi = ��0 + ��1(ABDOMENi ���90) + ��i
(a) Draw a scatterplot showing the relationship between abdominal girth and body fat. Show 95% con���dence and prediction bands. Does the plot suggest a linear
relationship between the variables? Explain brie���y. (b) When you run proc reg for the model above, SAS obtains estimates of three pa- rameters: ��0, ��1 and ��2. Fill in
the table below.
Model Point Concise Parameter Estimate Interpretation
��0
��1
��
(c) Construct the residual plot and the normal probability plot for residuals (similar to Figure 15.7 on p. 675). What do these plots suggest? (d) Report and interpret
the coef���cient of determination. (e) If you take a different sample of n = 252 male adults from the same population with the same abdominal girth values, are you
likely to obtain the same estimates of ��0, ��1 and ��2? (You���d better answer ���No.���) Because the estimates of these pa- rameters change from sample to sample, we say that
each of the estimates has a sampling distribution. i. What is an estimate of the standard deviation of the sampling distribution of b ��0? In other words, ���nd the
standard error of the statistic. ii. What is an estimate of the standard deviation of the sampling distribution of b ��1?
(f) In the proc reg output below, ���nd the t-value for ABDOMEN. Hint: Use the formula t = (b ��1 �����1)/SE(b ��1). Parameter Standard Variable DF Estimate Error t Value Pr
> |t| Abdomen 1 0.63130 0.02855 <.0001 (g) i. Usingtheformula,b ��1 �� t��SE(b ��1),���nda95%con���denceintervalfor ��1. (Note that for large n, t is close to 1.96.) Check your answer using the clb option in proc reg. ii. Doesthe95%con���denceintervalallowyoutoconcludethatthereisastatisti- cally signi���cant linear relationship between body fat percentage and abdomi- nal girth? Explain brie���y. (h) A researcher is interested in testing the null hypothesis that the population corre- lation coef���cient is zero. What is the value of the sample correlation coef���cient? Do you have reason to believe that the population correlation coef���cient is differ- ent from zero? What test statistic and p-value are you going to report? Explain. (Follow Example 15.11 in the textbook.) Obtain a 95% con���dence interval for ��. (i) ID 212 has an abdominal girth of 104.0 cm and body fat of 27.2. What is this subject���s residual? Interpret the value. (j) i. Predict the body fat of an adult male with abdominal girth = 117.0 cm. Note: There is no subject in the data set whose abdominal girth = 117.0 cm. ii. Reporta95%con���denceintervalforthemeanbodyfatofalladultmaleswith abdominal girth = 117 cm. Interpret the interval. iii. Report a 95% prediction interval for the body fat of an individual adult male with abdominal girth = 117 cm. Interpret the interval. iv. Which of the two intervals is wider? Did you expect this result? (k) i. Reporta99%con���denceintervalforthemeanbodyfatofalladultmaleswith abdominal girth = 75.0 cm. ii. Reporta99%con���denceintervalforthemeanbodyfatofalladultmaleswith abdominal girth = 95.0 cm. iii. Which of the two intervals is wider? Did you expect this result? ID %Fat - Brozek %Fat - Siri Density Age Weight Height Adiposity Fat Free Weight Neck Chest Abdomen Hip Thigh Knee Ankle Biceps Forearm Wrist 1 12.6 12.3 1.0708 23 154.25 67.75 23.7 134.9 36.2 93.1 85.2 94.5 59 37.3 21.9 32 27.4 17.1 2 6.9 6.1 1.0853 22 173.25 72.25 23.4 161.3 38.5 93.6 83 98.7 58.7 37.3 23.4 30.5 28.9 18.2 3 24.6 25.3 1.0414 22 154 66.25 24.7 116 34 95.8 87.9 99.2 59.6 38.9 24 28.8 25.2 16.6 4 10.9 10.4 1.0751 26 184.75 72.25 24.9 164.7 37.4 101.8 86.4 101.2 60.1 37.3 22.8 32.4 29.4 18.2 5 27.8 28.7 1.034 24 184.25 71.25 25.6 133.1 34.4 97.3 100 101.9 63.2 42.2 24 32.2 27.7 17.7 6 20.6 20.9 1.0502 24 210.25 74.75 26.5 167 39 104.5 94.4 107.8 66 42 25.6 35.7 30.6 18.8 7 19 19.2 1.0549 26 181 69.75 26.2 146.6 36.4 105.1 90.7 100.3 58.4 38.3 22.9 31.9 27.8 17.7 8 12.8 12.4 1.0704 25 176 72.5 23.6 153.6 37.8 99.6 88.5 97.1 60 39.4 23.2 30.5 29 18.8 9 5.1 4.1 1.09 25 191 74 24.6 181.3 38.1 100.9 82.5 99.9 62.9 38.3 23.8 35.9 31.1 18.2 10 12 11.7 1.0722 23 198.25 73.5 25.8 174.4 42.1 99.6 88.6 104.1 63.1 41.7 25 35.6 30 19.2 11 7.5 7.1 1.083 26 186.25 74.5 23.6 172.3 38.5 101.5 83.6 98.2 59.7 39.7 25.2 32.8 29.4 18.5 12 8.5 7.8 1.0812 27 216 76 26.3 197.7 39.4 103.6 90.9 107.7 66.2 39.2 25.9 37.2 30.2 19 13 20.5 20.8 1.0513 32 180.5 69.5 26.3 143.5 38.4 102 91.6 103.9 63.4 38.3 21.5 32.5 28.6 17.7 14 20.8 21.2 1.0505 30 205.25 71.25 28.5 162.5 39.4 104.1 101.8 108.6 66 41.5 23.7 36.9 31.6 18.8 15 21.7 22.1 1.0484 35 187.75 69.5 27.4 147 40.5 101.3 96.4 100.1 69 39 23.1 36.1 30.5 18.2 16 20.5 20.9 1.0512 35 162.75 66 26.3 129.3 36.4 99.1 92.8 99.2 63.1 38.7 21.7 31.1 26.4 16.9 17 28.1 29 1.0333 34 195.75 71 27.3 140.8 38.9 101.9 96.4 105.2 64.8 40.8 23.1 36.2 30.8 17.3 18 22.4 22.9 1.0468 32 209.25 71 29.2 162.5 42.1 107.6 97.5 107 66.9 40 24.4 38.2 31.6 19.3 19 16.1 16 1.0622 28 183.75 67.75 28.2 154.3 38 106.8 89.6 102.4 64.2 38.7 22.9 37.2 30.5 18.5 20 16.5 16.5 1.061 33 211.75 73.5 27.6 176.8 40 106.2 100.5 109 65.8 40.6 24 37.1 30.1 18.2 21 19 19.1 1.0551 28 179 68 27.3 145.1 39.1 103.3 95.9 104.9 63.5 38 22.1 32.5 30.3 18.4 22 15.3 15.2 1.064 28 200.5 69.75 29.1 169.8 41.3 111.4 98.8 104.8 63.4 40.6 24.6 33 32.8 19.9 23 15.7 15.6 1.0631 31 140.25 68.25 21.2 118.2 33.9 86 76.4 94.6 57.4 35.3 22.2 27.9 25.9 16.7 24 17.6 17.7 1.0584 32 148.75 70 21.4 122.6 35.5 86.7 80 93.4 54.9 36.2 22.1 29.8 26.7 17.1 25 14.2 14 1.0668 28 151.25 67.75 23.2 129.8 34.5 90.2 76.3 95.8 58.4 35.5 22.9 31.1 28 17.6 26 4.6 3.7 1.0911 27 159.25 71.5 21.9 151.9 35.7 89.6 79.7 96.5 55 36.7 22.5 29.9 28.2 17.7 27 8.5 7.9 1.0811 34 131.5 67.5 20.3 120.3 36.2 88.6 74.6 85.3 51.7 34.7 21.4 28.7 27 16.5 28 22.4 22.9 1.0468 31 148 67.5 22.9 114.9 38.8 97.4 88.7 94.7 57.5 36 21 29.2 26.6 17 29 4.7 3.7 1.091 27 133.25 64.75 22.4 127 36.4 93.5 73.9 88.5 50.1 34.5 21.3 30.5 27.9 17.2 30 9.4 8.8 1.079 29 160.75 69 23.8 145.7 36.7 97.4 83.5 98.7 58.9 35.3 22.6 30.1 26.7 17.6 31 12.3 11.9 1.0716 32 182 73.75 23.6 159.7 38.7 100.5 88.7 99.8 57.5 38.7 33.9 32.5 27.7 18.4 32 6.5 5.7 1.0862 29 160.25 71.25 22.2 149.8 37.3 93.5 84.5 100.6 58.5 38.8 21.5 30.1 26.4 17.9 33 13.4 11.8 1.0719 27 168 71.25 23.3 142.5 38.1 93 79.1 94.5 57.3 36.2 24.5 29 30 18.8 34 20.9 21.3 1.0502 41 218.5 71 30.5 172.7 39.8 111.7 100.5 108.3 67.1 44.2 25.2 37.5 31.5 18.7 35 31.1 32.3 1.0263 41 247.25 73.5 32.2 170.4 42.1 117 115.6 116.1 71.2 43.3 26.3 37.3 31.7 19.7 36 38.2 40.1 1.0101 49 191.75 65 32 118.4 38.4 118.5 113.1 113.8 61.9 38.3 21.9 32 29.8 17 37 23.6 24.2 1.0438 40 202.25 70 29.1 154.5 38.5 106.5 100.9 106.2 63.5 39.9 22.6 35.1 30.6 19 38 27.5 28.4 1.0346 50 196.75 68.25 29.7 142.6 42.1 105.6 98.8 104.8 66 41.5 24.7 33.2 30.5 19.4 39 33.8 35.2 1.0202 46 363.15 72.25 48.9 240.5 51.2 136.2 148.1 147.7 87.3 49.1 29.6 45 29 21.4 40 31.3 32.6 1.0258 50 203 67 31.8 139.4 40.2 114.8 108.1 102.5 61.3 41.1 24.7 34.1 31 18.3 41 33.1 34.5 1.0217 45 262.75 68.75 39.1 175.8 43.2 128.3 126.2 125.6 72.5 39.6 26.6 36.4 32.7 21.4 42 31.7 32.9 1.025 44 205 29.5 29.9 140.1 36.6 106 104.3 115.5 70.6 42.5 23.7 33.6 28.7 17.4 43 30.4 31.6 1.0279 48 217 70 31.2 151.1 37.3 113.3 111.2 114.1 67.7 40.9 25 36.7 29.8 18.4 44 30.8 32 1.0269 41 212 71.5 29.2 146.7 41.5 106.6 104.3 106 65 40.2 23 35.8 31.5 18.8 45 8.4 7.7 1.0814 39 125.25 68 19.1 114.7 31.5 85.1 76 88.2 50 34.7 21 26.1 23.1 16.1 46 14.1 13.9 1.067 43 164.25 73.25 21.3 141.1 35.7 96.6 81.5 97.2 58.4 38.2 23.4 29.7 27.4 18.3 47 11.2 10.8 1.0742 40 133.5 67.5 20.6 118.5 33.6 88.2 73.7 88.5 53.3 34.5 22.5 27.9 26.2 17.3 48 6.4 5.6 1.0665 39 148.5 71.25 20.6 139 34.6 89.8 79.5 92.7 52.7 37.5 21.9 28.8 26.8 17.9 49 13.4 13.6 1.0678 45 135.75 68.5 20.4 117.6 32.8 92.3 83.4 90.4 52 35.8 20.6 28.8 25.5 16.3 50 5 4 1.0903 47 127.5 66.75 20.2 121.2 34 83.4 70.4 87.2 50.6 34.4 21.9 26.8 25.8 16.8 51 10.7 10.2 1.0756 47 158.25 72.25 21.3 141.4 34.9 90.2 86.7 98.3 52.6 37.2 22.4 26 25.8 17.3 52 7.4 6.6 1.084 40 139.25 69 20.6 129 34.3 89.2 77.9 91 51.4 34.9 21 26.7 26.1 17.2 53 8.7 8 1.0807 51 137.25 67.75 21.1 125.3 36.5 89.7 82 89.1 49.3 33.7 21.4 29.6 26 16.9 54 7.1 6.3 1.0848 49 152.75 73.5 19.9 142 35.1 93.3 79.6 91.6 52.6 37.6 22.6 38.5 27.4 18.5 55 4.9 3.9 1.0906 42 136.25 67.5 21.1 129.6 37.8 87.6 77.6 88.6 51.9 34.9 22.5 27.7 27.5 18.5 56 22.2 22.6 1.0473 54 198 72 26.9 154.1 39.9 107.6 100 99.6 57.2 38 22 35.9 30.2 18.9 57 20.1 20.4 1.0524 58 181.5 68 27.6 145.1 39.1 100 99.8 102.5 62.1 39.6 22.5 33.1 28.3 18.5 58 27.1 28 1.0356 62 201.25 69.5 29.3 146.7 40.5 111.5 104.2 105.8 61.8 39.8 22.7 37.7 30.9 19.2 59 30.4 31.5 1.028 54 202.5 70.75 28.4 141 40.5 115.4 105.3 97 59.1 38 22.5 31.6 28.8 18.2 60 24 24.6 1.043 61 179.75 65.75 29.2 136.7 38.4 104.8 98.3 99.6 60.6 37.7 22.9 34.5 29.6 18.5 61 25.4 26.1 1.0396 62 216 73.25 28.2 161.2 41.4 112.3 104.8 103.1 61.6 40.9 23.1 36.2 31.8 20.2 62 28.8 29.8 1.0317 56 178.75 68.5 26.8 127.4 35.6 102.9 94.7 100.8 60.9 38 22.1 32.5 29.8 18.3 63 29.6 30.7 1.0298 54 193.25 70.25 27.6 136.1 38 107.6 102.4 99.4 61 39.4 23.6 32.7 29.9 19.1 64 25.1 25.8 1.0403 61 178 67 27.9 133.3 37.4 105.3 99.7 99.7 60.8 40.1 22.7 33.6 29 18.8 65 31 32.3 1.0264 57 205.5 70 29.5 141.7 40.1 105.3 105.5 108.3 65 41.2 24.7 35.3 31.1 18.4 66 28.9 30 1.0313 55 183.5 67.5 28.3 130.4 40.9 103 100.3 104.2 64.8 40.2 22.7 34.8 30.1 18.7 67 21.1 21.5 1.0499 54 151.5 70.75 21.3 119.6 35.6 90 83.9 93.9 55 36.1 21.7 29.6 27.4 17.4 68 14 13.8 1.0673 55 154.75 71.5 21.3 133.1 36.9 95.4 86.6 91.8 54.3 35.4 21.5 32.8 27.4 18.7 69 7.1 6.3 1.0847 54 155.25 69.25 22.8 144.2 37.5 89.3 78.4 96.1 56 37.4 22.4 32.6 28.1 18.1 70 13.2 12.9 1.0693 55 156.75 71.5 21.6 136.1 36.3 94.4 84.6 94.3 51.2 37.4 21.6 27.3 27.1 17.3 71 23.7 24.3 1.0439 62 167.5 71.5 23.1 127.8 35.5 97.6 91.5 98.5 56.6 38.6 22.4 31.5 27.3 18.6 72 9.4 8.8 1.0788 55 146.75 68.75 21.9 132.9 38.7 88.5 82.8 95.5 58.9 37.6 21.6 30.3 27.3 18.3 73 9.1 8.5 1.0796 56 160.75 73.75 20.8 146.1 36.4 93.6 82.9 96.3 52.9 37.5 23.1 29.7 27.3 18.2 74 13.7 13.5 1.068 55 125 64 21.5 107.9 33.2 87.7 76 88.6 50.9 35.4 19.1 29.3 25.7 16.9 75 12 11.8 1.072 61 143 65.75 23.3 125.9 36.5 93.4 83.3 93 55.5 35.2 20.9 29.4 27 16.8 76 18.3 18.5 1.0666 61 148.25 67.5 22.9 121.1 36 91.6 81.8 94.8 54.5 37 21.4 29.3 27 18.3 77 9.2 8.8 1.079 57 162.5 69.5 23.7 147.5 38.7 91.6 78.8 94.3 56.7 39.7 24.2 30.2 29.2 18.1 78 21.7 22.2 1.0483 69 177.75 68.5 26.7 139.1 38.7 102 95 98.3 55 38.3 21.8 30.8 25.7 18.8 79 21.1 21.5 1.0498 81 161.25 70.25 23 127.2 37.8 96.4 95.4 99.3 53.5 37.5 21.5 31.4 26.8 18.3 80 18.6 18.8 1.056 66 171.25 69.25 25.1 139.5 37.4 102.7 98.6 100.2 56.5 39.3 22.7 30.3 28.7 19 81 30.2 31.4 1.0283 67 163.75 67.75 25.1 114.3 38.4 97.7 95.8 97.1 54.8 38.2 23.7 29.4 27.2 19 82 26 26.8 1.0382 64 150.25 67.25 23.4 111.2 38.1 97.1 89 96.9 54.8 38 22 29.9 25.2 17.7 83 18.2 18.4 1.0568 64 190.25 72.75 25.3 155.6 39.3 103.1 97.8 99.6 58.9 39 23 34.3 29.6 19 84 26.2 27 1.0377 70 170.75 70 24.5 126 38.7 101.8 94.9 95 56 36.5 24.1 31.2 27.3 19.2 85 26.1 27 1.0378 72 168 69.25 24.7 124.1 38.5 101.4 99.8 96.2 56.3 36.6 22 29.7 26.3 18 86 25.8 26.6 1.0386 67 167 67.5 26 123.9 36.5 98.9 89.7 96.2 54.7 37.8 33.7 32.4 27.7 18.2 87 15 14.9 1.0648 72 157.75 67.25 24.6 134.1 37.7 97.5 88.1 96.9 57.2 37.7 21.8 32.6 28 18.8 88 22.6 23.1 1.0462 64 160 65.75 26 123.8 36.5 104.3 90.9 93.8 57.8 39.5 23.3 29.2 28.4 18.1 89 8.8 8.3 1.08 46 176.75 72.5 23.7 161.1 38 97.3 86 99.3 61 38.4 23.8 30.2 29.3 18.8 90 14.3 14.1 1.0666 48 176 73 23.3 150.9 36.7 96.7 86.5 98.3 60.4 39.9 24.4 28.8 29.6 18.7 91 20.2 20.5 1.052 46 177 70 25.4 141.3 37.2 99.7 95.6 102.2 58.3 38.2 22.5 29.1 27.7 17.7 92 18.1 18.2 1.0573 44 179.75 69.5 26.2 147.3 39.2 101.9 93.2 100.6 58.9 39.7 23.1 31.4 28.4 18.8 93 9.2 8.5 1.0795 47 165.25 70.5 23.4 150.1 37.5 97.2 83.1 95.4 56.9 38.3 22.1 30.1 28.2 18.4 94 24.2 24.9 1.0424 46 192.5 71.75 26.3 145.9 38 106.6 97.5 100.6 58.9 40.5 24.5 33.3 29.6 19.1 95 9.6 9 1.0785 47 184.25 74.5 23.4 166.6 37.3 99.6 88.8 101.4 57.4 39.6 24.6 30.3 27.9 17.8 96 17.3 17.4 1.0991 53 224.5 77.75 26.1 185.7 41.1 113.2 99.2 107.5 61.7 42.3 23.2 32.9 30.8 20.4 97 10.1 9.6 1.077 38 188.75 73.25 24.8 169.6 37.5 99.1 91.6 102.4 60.6 39.4 22.9 31.6 30.1 18.5 98 11.1 11.3 1.073 50 162.5 66.5 25.9 143.5 38.7 99.4 86.7 96.2 62.1 39.3 23.3 30.6 27.8 18.2 99 17.7 17.8 1.0582 46 156.5 68.25 23.7 128.8 35.9 95.1 88.2 92.8 54.7 37.3 21.9 31.6 27.5 18.2 100 21.7 22.2 1.0484 47 197 72 26.7 154.2 40 107.5 94 103.7 62.7 39 22.3 35.3 30.9 18.3 101 20.8 21.2 1.0506 49 198.5 73.5 25.9 157.2 40.1 106.5 95 101.7 59 39.4 22.3 32.2 31 18.6 102 20.1 20.4 1.0524 48 173.75 72 23.6 138.9 37 99.1 92 98.3 59.3 38.4 22.4 27.9 26.2 17 103 19.8 20.1 1.053 41 172.75 71.25 24 138.6 36.3 96.7 89.2 98.3 60 38.4 23.2 31 29.2 18.4 104 21.9 22.3 1.048 49 196.75 73.75 25.5 153.7 40.7 103.5 95.5 101.6 59.1 39.8 25.4 31 30.3 19.7 105 24.7 25.4 1.0412 43 177 69.25 26 133.2 39.6 104 98.6 99.5 59.5 36.1 22 30.1 27.2 17.7 106 17.8 18 1.0578 43 165.5 68.5 24.8 136 31.1 93.1 87.3 96.6 54.7 39 24.8 31 29.4 18.8 107 19.1 19.3 1.0547 43 200.25 73.5 26 162 38.6 105.2 102.8 103.6 61.2 39.3 23.5 30.5 28.5 18.1 108 18.2 18.3 1.0569 52 203.25 74.25 26 166.3 42 110 101.6 100.7 55.8 38.7 23.4 35.1 29.6 19.1 109 17.2 17.3 1.0593 43 194 75.5 24 160.6 38.5 110.1 88.7 102.1 57.5 40 24.8 35.1 30.7 19.2 110 21 21.4 1.05 40 168.5 69.25 24.7 133.1 34.2 97.8 92.3 100.6 57.5 36.8 22.8 32.1 26 17.3 111 19.5 19.7 1.0538 43 170.75 68.5 25.6 137.5 37.2 96.3 90.6 99.3 61.9 38 22.3 33.3 28.2 18.1 112 27.1 28 1.0355 43 183.25 70 26.3 133.5 37.1 108 105 103 63.7 40 23.6 33.5 27.8 17.4 113 21.6 22.1 1.0486 47 178.25 70 25.6 139.7 40.2 99.7 95 98.6 62.3 38.1 23.9 35.3 31.1 19.8 114 20.9 21.3 1.0503 42 163 70.25 23.3 128.9 35.3 93.5 89.6 99.8 61.5 37.8 21.9 30.7 27.6 17.4 115 25.9 26.7 1.0384 48 175.25 71.75 24 129.9 38 100.7 92.4 97.5 59.3 38.1 21.8 31.8 27.3 17.5 116 16.7 16.7 1.0607 40 158 69.25 23.4 131.7 36.3 97 86.6 92.6 55.9 36.3 22.1 29.8 26.3 17.3 117 19.8 20.1 1.0529 48 177.25 72.75 23.6 142.1 36.8 96 90 99.7 58.8 38.4 22.8 29.9 28 18.1 118 14.1 13.9 1.0671 51 179 72 24.3 153.8 41 99.2 90 96.4 56.8 38.8 23.3 33.4 29.8 19.5 119 25.1 25.8 1.0404 40 191 74 24.6 143.1 38.3 95.4 92.4 104.3 64.6 41.1 24.8 33.6 29.5 18.5 120 17.9 18.1 1.0575 44 187.5 72.25 25.3 153.8 38 101.8 87.5 101 58.5 39.2 24.5 32.1 28.6 18 121 27 27.9 1.0358 52 206.5 74.5 26.2 150.7 40.8 104.3 99.2 104.1 58.5 39.3 24.6 33.9 31.2 19.5 122 24.6 25.3 1.0414 44 185.25 71.5 25.5 139.6 39.5 99.2 98.1 101.4 57.1 40.5 23.2 33 29.6 18.4 123 14.8 14.7 1.0652 40 160.25 68.75 23.9 136.5 36.9 99.3 83.3 97.5 60.5 38.7 22.6 34.4 28 17.6 124 16 16 1.0623 47 151.5 66.75 23.9 127.3 36.9 94 86.1 95.2 58.1 36.5 22.1 30.6 27.5 17.6 125 14 13.8 1.0674 50 161 66.5 25.6 138.5 37.7 98.9 84.1 94 58.5 36.6 23.5 34.4 29.2 18 126 17.4 17.5 1.0587 46 167 67 26.2 137.9 36.6 101 89.9 100 60.7 36 21.9 35.6 30.2 17.6 127 26.4 27.2 1.0373 42 177.5 68.75 26.4 130.7 38.9 98.7 92.1 98.5 60.7 36.8 22.2 33.8 30.3 17.2 128 17.4 17.4 1.059 43 152.25 67.75 23.4 125.8 37.5 95.9 78 93.2 53.5 35.8 20.8 33.9 28.2 17.4 129 20.4 20.8 1.0515 40 192.25 73.25 25.2 153 39.8 103.9 93.5 99.5 61.7 39 21.8 33.3 29.6 18.1 130 15 14.9 1.0648 42 165.25 69.75 23.9 140.5 38.3 96.2 87 97.8 57.4 36.9 22.2 31.6 27.8 17.7 131 18 18.1 1.0575 49 171.75 71.5 23.7 140.9 35.5 97.8 90.1 95.8 57 38.7 23.2 27.5 26.5 17.6 132 22.2 22.7 1.0472 40 171.25 70.5 24.3 133.3 36.3 94.6 90.3 99.1 60.3 38.5 23 31.2 28.4 17.1 133 23.1 23.6 1.0452 47 197 73.25 25.8 151.2 37.8 103.6 99.8 103.2 61.2 38.1 22.6 33.5 28.6 17.9 134 25.3 26.1 1.0398 50 157 66.75 24.8 117.2 37.8 100.4 89.4 92.3 56.1 35.6 20.5 33.6 29.3 17.3 135 23.8 24.4 1.0435 41 168.25 69.5 24.5 128.3 36.5 98.4 87.2 98.4 56 36.9 23 34 29.8 18.1 136 26.3 27.1 1.0374 44 186 69.75 26.8 137.1 37.8 104.6 101.1 102.1 58.9 37.9 22.7 30.9 28.8 17.6 137 21.4 21.8 1.0491 39 166.75 70.75 23.5 131 37 92.9 86.1 95.6 58.8 36.1 22.4 32.7 28.3 17.1 138 28.4 29.4 1.0325 43 187.75 74 24.1 134.4 37.7 97.8 98.6 100.6 63.6 39.2 23.8 34.3 28.4 17.7 139 21.8 22.4 1.0481 40 168.25 71.25 23.3 131.6 34.3 98.3 88.5 98.3 58.1 38.4 22.5 31.7 27.4 17.6 140 20.1 20.4 1.0522 49 212.75 75 26.6 169.9 40.8 104.7 106.6 107.7 66.5 42.5 24.5 35.5 29.8 18.7 141 24.3 24.9 1.0422 40 176.75 71 24.6 133.8 37.4 98.6 93.1 101.6 59.1 39.6 21.6 30.8 27.9 16.6 142 18.1 18.3 1.0571 40 173.25 69.5 25.3 141.8 36.5 99.5 93 99.3 60.4 38.2 22 32 28.5 17.8 143 22.7 23.3 1.0459 52 167 67.75 25.6 129 37.5 102.7 91 98.9 57.1 36.7 22.3 31.6 27.5 17.9 144 9.9 9.4 1.0775 23 159.75 72.25 21.6 143.9 35.5 92.1 77.1 93.9 56.1 36.1 22.7 30.5 27.2 18.2 145 10.8 10.3 1.0754 23 188.15 77.5 22.1 168.4 38 96.6 85.3 102.5 59.1 37.6 23.2 31.8 29.7 18.3 146 14.4 14.2 1.0664 24 156 70.75 21.9 133.6 35.7 92.7 81.9 95.3 56.4 36.5 22 33.5 28.3 17.3 147 19 19.2 1.055 24 208.5 72.75 27.7 168.9 39.2 102 99.1 110.1 71.2 43.5 25.2 36.1 30.3 18.7 148 28.6 29.6 1.0322 25 206.5 69.75 29.8 147.5 40.9 110.9 100.5 106.2 68.4 40.8 24.6 33.3 29.7 18.4 149 6.1 5.3 1.0873 25 143.75 72.5 19.3 135 35.2 92.3 76.5 92.1 51.9 35.7 22 25.8 25.2 16.9 150 24.5 25.2 1.0416 26 223 70.25 31.8 168.3 40.6 114.1 106.8 113.9 67.6 42.7 24.7 36 30.4 18.4 151 9.9 9.4 1.0776 26 152.25 69 22.5 137.2 35.4 92.9 77.6 93.5 56.9 35.9 20.4 31.6 29 17.8 152 19.1 19.6 1.0542 26 241.75 74.5 30.7 195.1 41.8 108.3 102.9 114.4 72.9 43.5 25.1 38.5 33.8 19.6 153 10.6 10.1 1.0758 27 146 72.25 19.7 130.5 34.1 88.5 72.8 91.1 53.6 36.8 23.8 27.8 26.3 17.4 154 16.5 16.5 1.061 27 156.75 67.25 24.4 130.9 37.9 94 88.2 95.2 56.8 37.4 22.8 30.6 28.3 17.9 155 20.5 21 1.051 27 200.25 73.5 26.1 159.3 38.2 101.1 100.1 105 62.1 40 24.9 33.7 29.2 19.4 156 17.2 17.3 1.0594 28 171.5 75.25 21.6 142 35.6 92.1 83.5 98.3 57.3 37.8 21.7 32.2 27.7 17.7 157 30.1 31.2 1.0287 28 205.75 69 30.4 143.9 38.5 105.6 105 106.4 68.6 40 25.2 35.2 30.7 19.1 158 10.5 10 1.0761 28 182.5 72.25 24.6 163.4 37 98.5 90.8 102.5 60.8 38.5 25 31.6 28 18.6 159 12.8 12.5 1.0704 30 136.5 68.75 20.3 119.1 35.9 88.7 76.6 89.8 50.1 34.8 21.8 27 34.9 16.9 160 22 22.5 1.0477 31 177.25 71.5 24.4 138.3 36.2 101.1 92.4 99.3 59.4 39 24.6 30.1 28.2 18.2 161 9.9 9.4 1.0775 31 151.25 72.25 20.4 136.2 35 94 81.2 91.5 52.5 36.6 21 27 26.3 16.5 162 14.8 14.6 1.0653 33 196 73 25.9 167 38.5 103.8 95.6 105.1 61.4 40.6 25 31.3 29.2 19.1 163 13.3 13 1.069 33 184.25 68.75 24.4 159.8 40.7 98.9 92.1 103.5 64 37.3 23.5 33.5 30.6 19.7 164 15.2 15.1 1.0644 34 140 70.5 19.8 118.8 36 89.2 83.4 89.6 52.4 35.6 20.4 28.3 26.2 16.5 165 26.5 27.3 1.037 34 218.75 72 29.7 160.8 39.5 111.4 106 108.8 63.8 42 23.4 34 31.2 18.5 166 19 19.2 1.0549 35 217 73.75 28.1 175.8 40.5 107.5 95.1 104.5 64.8 41.3 25.6 36.4 33.7 19.4 167 21.4 21.8 1.0492 35 166.25 68 25.3 130.7 38.5 99.1 90.4 95.6 55.5 34.2 21.9 30.2 28.7 17.7 168 20 20.3 1.0525 35 224.75 72.25 30.3 179.7 43.9 108.2 100.4 106.8 63.3 41.7 24.6 37.2 33.1 19.8 169 34.7 34.3 1.018 35 228.25 69.5 33.3 149.3 40.4 114.9 115.9 111.9 74.4 40.6 24 36.1 31.8 18.8 170 16.5 16.5 1.061 35 172.75 69.5 25.2 144.2 37.6 99.1 90.8 98.1 60.1 39.1 23.4 32.5 29.8 17.4 171 4.1 3 1.0926 35 152.25 67.75 23.4 146.1 37 92.2 81.9 92.8 54.7 36.2 22.1 30.4 27.4 17.7 172 1.9 0.7 1.0983 35 125.75 65.5 20.6 123.4 34 90.8 75 89.2 50 34.8 22 24.8 25.9 16.9 173 20.2 20.5 1.0521 35 177.25 71 24.8 141.7 38.4 100.5 90.3 98.7 57.8 37.3 22.4 31 28.7 17.7 174 16.8 16.9 1.0603 36 176.25 71.5 24.3 146.6 38.7 98.2 90.3 99.9 59.2 37.7 21.5 32.4 28.4 17.8 175 24.6 25.3 1.0414 36 226.75 71.75 31 170.9 41.5 115.3 108.8 114.4 69.2 42.4 24 35.4 21 20.1 176 10.4 9.9 1.0763 37 145.25 69.25 21.3 130.2 36 96.8 79.4 89.2 50.3 34.8 22.2 31 26.9 16.9 177 13.4 13.1 1.0689 37 151 67 23.7 130.8 35.3 92.6 83.2 96.4 60 38.1 22 31.5 26.6 16.7 178 28.8 29.9 1.0316 37 241.25 71.5 33.2 171.7 42.1 119.2 110.3 113.9 69.8 42.6 24.8 34.4 29.5 18.4 179 22 22.5 1.0477 38 187.25 69.25 27.5 146.1 38 102.7 92.7 101.9 64.7 39.5 24.7 34.8 30.3 18.1 180 16.8 16.9 1.0603 39 234.75 74.5 29.8 195.3 42.8 109.5 104.5 109.9 69.5 43.1 25.8 39.1 32.5 19.9 181 25.8 26.6 1.0387 39 219.25 74.25 28 162.7 40 108.5 104.6 109.8 68.1 42.8 24.1 35.6 29 19 182 0 0 1.1089 40 118.5 68 18.1 118.5 33.8 79.3 69.4 85 47.2 33.5 20.2 27.7 24.6 16.5 183 11.9 11.5 1.0725 40 145.75 67.25 22.7 128.4 35.5 95.5 83.6 91.6 54.1 36.2 21.8 31.4 28.3 17.2 184 12.4 12.1 1.0713 40 159.25 69.75 23 139.5 35.3 92.3 86.8 96.1 58 39.4 22.7 30 26.4 17.4 185 17.4 17.5 1.0587 40 170.5 74.25 21.8 140.8 37.7 98.9 90.4 95.5 55.4 38.9 22.4 30.5 28.9 17.7 186 9.2 8.6 1.0794 40 167.5 71.5 23.1 152.1 39.4 89.5 83.7 98.1 57.3 39.7 22.6 32.9 29.3 18.2 187 23 23.6 1.0453 41 232.75 74.25 29.7 179.2 41.9 117.5 109.3 108.8 67.7 41.3 24.7 37.2 31.8 20 188 20.1 20.4 1.0524 41 210.5 72 28.6 168.3 38.5 107.4 98.9 104.1 63.5 39.8 23.5 36.4 30.4 19.1 189 20.2 20.5 1.052 41 202.25 72.5 27 161.4 40.8 109.2 98 101.8 62.8 41.3 24.8 36.6 32.4 18.8 190 23.8 24.4 1.0434 41 185 68.25 28 141 38 103.4 101.2 103.1 61.5 40.4 22.9 33.4 29.2 18.5 191 11.8 11.4 1.0728 41 153 69.25 22.5 135 36.4 91.4 80.6 92.3 54.3 36.3 21.8 29.6 27.3 17.9 192 36.5 38.1 1.014 42 244.25 76 29.8 155.2 41.8 115.2 113.7 112.4 68.5 45 25.5 37.1 31.2 19.9 193 16 15.9 1.0624 42 193.5 70.5 27.4 162.6 40.7 104.9 94.1 102.7 60.6 38.6 24.7 34 30.1 18.7 194 24 24.7 1.0429 42 224.75 74.75 28.3 170.8 38.5 106.7 105.7 111.8 65.3 43.3 26 33.7 29.9 18.5 195 22.3 22.8 1.047 42 162.75 72.75 21.6 126.5 35.4 92.2 85.6 96.5 60.2 38.9 22.4 31.7 27.1 17.1 196 24.8 25.5 1.0411 42 180 68.25 27.2 135.4 38.5 101.6 96.6 100.6 61.1 38.4 24.1 32.9 29.8 18.8 197 21.5 22 1.0488 42 156.25 69 23.1 122.6 35.5 97.8 86 96.2 57.7 38.6 24 31.2 27.3 17.4 198 17.6 17.7 1.0583 42 168 71.5 23.1 138.4 36.5 92 89.7 101 62.3 38 22.3 30.8 27.8 16.9 199 7.3 6.6 1.0841 42 167.25 72.75 22.3 155.1 37.6 94 78 99 57.5 40 22.5 30.6 30 18.5 200 22.6 23.6 1.0462 43 170.75 67.5 26.4 132.1 37.4 103.7 89.7 94.2 58.5 39 24.1 33.8 28.8 18.8 201 12.5 12.2 1.0709 43 178.25 70.25 25.4 155.9 37.8 102.7 89.2 99.2 60.2 39.2 23.8 31.7 28.4 18.6 202 21.7 22.1 1.0484 43 150 69.25 22 117.5 35.2 91.1 85.7 96.9 55.5 35.7 22 29.4 26.6 17.4 203 27.7 28.7 1.034 43 200.5 71.5 27.6 144.9 37.9 107.2 103.1 105.5 68.8 38.3 23.7 32.1 28.9 18.7 204 6.8 6 1.0854 44 184 74 23.7 171.4 37.9 100.8 89.1 102.6 60.6 39 24 32.9 29.2 18.4 205 33.4 34.8 1.0209 44 223 69.75 32.3 148.5 40.9 121.6 113.9 107.1 63.5 40.3 21.8 34.8 30.7 17.4 206 16.6 16.6 1.061 44 208.75 73 27.6 174.2 41.9 105.6 96.3 102 63.3 39.8 24.1 37.3 23.1 19.4 207 31.7 32.9 1.025 44 166 65.5 27.2 113.5 39.1 100.6 93.9 100.1 58.9 37.6 21.4 33.1 29.5 17.3 208 31.5 32.8 1.0254 47 195 72.5 26.1 133.6 40.2 102.7 101.3 101.7 60.7 39.4 23.3 36.7 31.6 18.4 209 10.1 9.6 1.0771 47 160.5 70.25 22.9 144.3 36 99.8 83.9 91.8 53 36.2 22.5 31.4 27.5 17.7 210 11.3 10.8 1.0742 47 159.75 70.75 22.5 141.8 34.5 92.9 84.4 94 56 38.2 22.6 29 26.2 17.6 211 7.8 7.1 1.0829 49 140.5 68 21.4 129.5 35.8 91.2 79.4 89 51.1 35 21.7 30.9 28.8 17.4 212 26.4 27.2 1.0373 49 216.25 74.5 27.4 159.3 40.2 115.6 104 109 63.7 40.3 23.2 36.8 31 18.9 213 19.3 19.5 1.0543 49 168.25 71.75 23 135.9 38.3 98.3 89.7 99.1 56.3 38.8 23 29.5 27.9 18.6 214 18.5 18.7 1.0561 50 194.75 70.75 27.4 158.7 39 103.7 97.6 104.2 60 40.9 25.5 32.7 30 19 215 19.3 19.5 1.0543 50 172.75 73 22.8 139.4 37.4 98.7 87.6 96.1 57.1 38.1 21.8 28.6 26.7 18 216 45.1 47.5 0.995 51 219 64 37.6 120.2 41.2 119.8 122.1 112.8 62.5 36.9 23.6 34.7 29.1 18.4 217 13.8 13.6 1.0678 51 149.25 69.75 21.6 128.7 34.8 92.8 81.1 96.3 53.8 36.5 21.5 31.3 26.3 17.8 218 8.2 7.5 1.0819 51 154.5 70 22.2 141.9 36.9 93.3 81.5 94.4 54.7 39 22.6 27.5 25.9 18.6 219 23.9 24.5 1.0433 52 199.25 71.75 27.2 151.7 39.4 106.8 100 105 63.9 39.2 22.9 35.7 30.4 19.2 220 15.1 15 1.0646 53 154.5 69.25 22.7 131.2 37.6 93.9 88.7 94.5 53.7 36.2 22 28.5 25.7 17.1 221 12.7 12.4 1.0706 54 153.25 70.5 24.5 151.3 38.5 99 91.8 96.2 57.7 38.1 23.9 31.4 29.9 18.9 222 25.3 26 1.0399 54 230 72.25 31 171.9 42.5 119.9 110.4 105.5 64.2 42.7 27 38.4 32 19.6 223 11.9 11.5 1.0726 54 161.75 67.5 25 142.6 37.4 94.2 87.6 95.6 59.7 40.2 23.4 27.9 27 17.8 224 6.1 5.2 1.0874 55 142.25 67.25 22.2 133.6 35.2 92.7 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